More about the origin of the notation Sigma_i and Pi_i for the different
levels of the arithmetic hierarchy... I can now at least recall a
reference:
Kleene (who had himself introduced the the levels of arithmetical hierarchy
in 1943) wrote, in his introductory note to Gödel's 1930b, 1931 and 1932b
(in Gödel's Collected Works I, page 133, footnote f), that the
metamathematical use of the notations Sigma^0_i and Pi^0_i to describe the
levels in the arithmetical hierarchy were introduced by Addison 1958 and
Mostowski 1959.
Best
Panu Raatikainen
PhD., Docent in Theoretical Philosophy
Fellow, Helsinki Collegium for Advanced Studies
University of Helsinki
Address:
Helsinki Collegium for Advanced Studies
P.O. Box 4
FIN-00014 University of Helsinki
Finland
E-mail: panu.raatikainen at helsinki.fihttp://www.helsinki.fi/collegium/eng/Raatikainen/raatikainen.htm